MANHATTAN, Kan. -- Kansas State's Jack Cantele had never tried a game-winning field goal, not as a kid growing up in Wichita or as the star kicker at Kapaun Mt. Carmel High School.

In his words, he'd been waiting his whole life for the opportunity.

So when the sophomore drilled a 41-yarder with 3 seconds remaining Saturday, his fourth field goal of the game, he leaped into the air in a wild celebration. The kick gave the Wildcats a 33-31 victory over TCU and made them bowl eligible for the fourth straight season.

"There was no doubt it was going in. It was one of the best kicks I've ever kicked," said Cantele, whose older brother Anthony also kicked for Kansas State.

"I didn't know how to react," Cantele said. "Someone hit me from behind and I fell to the ground, and I just started beating the crap out of the ground. I didn't know what else to do."

Kansas State (6-4, 4-3 Big 12) was flagged for excessive celebration when several players ran off the bench. But the 15-yard penalty didn't matter. TCU (4-7, 2-6) couldn't do anything with the ensuing kickoff as Kansas State wrapped up its fourth straight win.

"The bottom line is we didn't play nearly as well as I'd like us to play," Kansas State coach Bill Snyder said, "but we played well enough to win."

Just barely, though. The Wildcats squandered a 17-7 halftime lead, and then watched as the Horned Frogs' Jaden Oberkrom hit a 56-yard field goal to give TCU a 31-30 lead with 2:13 left.

Kansas State took over and Jake Waters deftly marched his team down field, hitting Tyler Lockett for 12 yards to convert a third down, and then hitting him again for 8 more yards. That was enough to get Cantele within range of the go-ahead field goal.

"It was just a great ballgame," TCU coach Gary Patterson said.

Not such a great return to his alma mater. Patterson grew up in tiny Rozel, Kan., and played for the Wildcats from 1980-81. He said he hadn't been back in years.

The stinging defeat left his team ineligible for a bowl game for the first time since 2004.

"This is only the second time in 16 years that we haven't been to a bowl game," Patterson said. "We've got two weeks and we've got an opportunity to play a Baylor team at home. It won't be a bowl game, so the Baylor game will have to be our bowl game."

The Wildcats jumped out to an early lead when Daniel Sams, alternating with Waters at quarterback, scooted 11 yards for a touchdown. A few minutes later, Waters hit Lockett -- who had beaten All-American cornerback Jason Verrett -- with a 74-yard touchdown pass.

TCU finally got going when B.J. Catalon left Kansas State safety Dante Barnett grasping for air on a 15-yard TD run. But the Wildcats answered Cantele's field-goal for a 17-7 halftime lead.

The Horned Frogs pulled ahead in the second half when Trevone Boykin hit Josh Dotson in the back of the end zone from a yard out. After a fumble by Sams, Boykin carried around the left side on fourth-and-1 from the Kansas State 7 for a touchdown and a 21-17 lead.

In a game of wild momentum swings, Kansas State quickly took it back.

On third-and-14 from the Wildcats' 21-yard line, Waters took advantage of time in the pocket to hit Tramaine Thompson in broken coverage. He out-ran safety Elisha Olabode to the end zone for a 24-21 lead -- the 79-yard scoring strike the longest for Kansas State since 2005.

Back came the Horned Frogs, who went after backup safety Dylan Schellenberg, pressed into duty after an injury to Ty Zimmerman. David Porter ran past Schellenberg and caught Pachall's 51-yard touchdown pass to give TCU a 28-24 lead late in the third quarter.

Cantele added a field goal to pull within a point, and then Kansas State took advantage of a bizarre penalty to take the lead in the fourth quarter. The Horned Frogs were whistled for having two players wearing No. 2 on the field during a punt, giving Kansas State a fourth-and-1, which they converted for a first down. The drive ended with Cantele kicking a 23-yard field goal for a 30-28 lead.

"It's the first time where that's ever happened," Patterson said of the penalty.

The Horned Frogs marched to the Kansas State 39 on their ensuing possession, but defensive end Alauna Finau got his hand on Pachall's pass on third-and-5. Patterson decided to send Oberkrom onto the field rather than punt, and his 56-yard field goal had a few yards to spare.

It turned out, though, that the Horned Frogs left too much time on the clock.

"After the field goal, I had a lot of faith in our defense," Pachall said. "But we really shouldn't have put them in that situation and put all of the pressure on them."